Name:
Period:
C
College Algebra: Expos and Logs Test (4.5 - 4.8)
You must show supporting work on all problems to receive credit. Calculators are required.
I  Pr t
r

A  P0 1  
n

nt
A  A0 e kt
A  P0 e rt
 t   T   0  T e kt
In problems 1 - 5, choose the one alternative that best completes the statement or answers the question.
Supporting work/reasoning must be shown in order to receive credit for your answer. (+2 ea)
1. Evaluate by using properties of logarithms. (3 ln 6  2 ln 4)  ln 48
1. ______
1. ________
(+2)
A.
B.
C.
D.
E.
ln 3
ln 36
ln 12
ln 72
None of the above
2. The half-life of radioactive cobalt is 4.9 years. If a sample presently contains 120 grams of radioactive
cobalt now, how much will be present in 25 years?
2. ______
A.
B.
C.
D.
E.
57.2 grams
58.3 grams
61.7 grams
60.5 grams
None of the above
3. The formula D  8e 0.6 h can be used to find the number of milligrams D of a certain drug that is in a patient's
bloodstream h hours after the drug has been administered. The drug is to be administered again when the
amount in the bloodstream reaches 5 milligrams. What is the time between injections?
A.
B.
C.
D.
E.
about 0.8 of an hour
about 1.5 hours
about 0.7 of an hour
about 1.1 hours
None of the above
3. ______
4. If log 7 2  a, log 7 3  b , and log 7 5  c , log 7 
2
45 
 can be written in terms of a, b, and c as
 4 
4b + c - 4a
4b + 2c- 4a
2b + 2c - 4a
4b + 2c - 2a
None of the above
5. What is the effective rate of interest for 10% compounded daily?
4. ______
A.
B.
C.
D.
A.
A.
B.
C.
D.
E.
10.81%
10.76%
10.25%
10.52%
None of the above
5. ________(+2)
Solve the following logarithmic equations algebraically. No decimal answers will be accepted.
6. 2 log 4 ( x  3)  log 4 8  2
7. ln 12  ln( 7  x)  ln x
6. __________ (+5)
7. __________ (+5)
8. log 5 x  2  log 5 (2 x  1)  log 10
9. 3 log 5 x  log 25 x  14
8. __________ (+5)
9. __________ (+5)
Solve the following exponential equations algebraically. If applicable, give logarithmic answers in terms of
natural log, ln. Combine log expressions to a single logarithm when applicable.
10. 5 3 x  4 3 x 1
11.
e x  6e  x
1
5
10. _________________ (+5)
11. _________________ (+5)
12. 9  3
x
x2
 20  0
2 x 1
13. 8  4 
32
x
x
12. _________________ (+5)
13. _________________ (+5)
14. Write as a sum and/or difference of logarithms. Express all powers as factors, factor completely, and
combine like terms.

 (3x  6) 4 x 2  1
ln 
3
 x 2  x  2




14. ______________________________________________________________________ (+5)
In 15 - 17, to receive credit for your answer, you must clearly state all work/formulas used and show all
work required to support your answer.
15. Assume the average selling price of a home in Fort Collins grows according to uninhibited exponential
growth. If the average selling price of a home was $25,600 at the start of 1976 and it was $226,400 at the start
of 2007, what can you predict the average selling price of a home in Fort Collins will be in the year 2030?
Round to the nearest dollar.
15. _____________________ (+3)
16. Assume your parents invest $15,000 into a stock fund when you are born to be used for your college
education. The investment does well, on average, and the value grows at 6% compounded monthly. Show all
formulas and work necessary in order to receive credit for your answers.
a) How much will the investment be worth on your 18th birthday? Round to the nearest dollar.
a) ______________ (+2)
b) How many years will it take for the bond to double in value? Round to one decimal place.
b) _____________ (+2)
c) How much would you have had to invest initially in order for the investment to be worth $50,000 on your
18th birthday? Round to the nearest dollar.
c) ______________ (+2)
d) If instead, the investment is compounded continuously at 6%, how many years will it take for the investment
to triple in value? Round to one decimal place.
d) _____________ (+2)
17. “Bananas Foster” is a dessert served flambe' style at your table featuring banana slices cooked in a vanilla,
brown sugar, and cinnamon cream sauce. Assume the heated banana slices are initially 350 °F and the room
temperature is 65 °F. After 5 minutes, the temperature of the bananas is 225 °F. If you cannot eat the banana
slices until they cool to 150 °F, how many minutes will you have to wait before you can eat your dessert?
Round answer to the nearest minute.
17. _____________________ (+3)